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本文研究了含有不确定参数的非线性大系统的稳定性,当参数向量受到限制时,这种稳定性称为鲁棒(粗壮)稳定性。在状态空间的含原点的有限域中,利用李亚普诺夫函数进行集结线性化,可将大系统化为线性系统。由于线性化的任意性,得到的线性系统不是唯一的。文中阐明了利用图论方法建立的大系统的多层结构可以简化稳定性判据,帮助选择局部反馈,以实现大系统的镇定。
In this paper, we study the stability of nonlinear large-scale systems with uncertain parameters. When the parameter vector is limited, this stability is called robust (robust) stability. In the finite field containing the origin of the state space, the system is linearized by the Lyapunov function, which can be systematically transformed into a linear system. Due to the arbitrariness of linearization, the resulting linear system is not unique. In this paper, the multi-layer structure of large system established by graph theory is illustrated to simplify the stability criterion and help to select local feedback in order to achieve the stabilization of large-scale system.